The pair of equations x = 0 and x = 7 has:

(a) two solutions

(b) no solution

(c) infinitely many solutions

(d) one solution

In the equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\), if \({\frac{a_1}{a_2}}\ne{\frac{b_1}{b_2}}\), then the equations will represent:

(a) coincident lines

(b) parallel lines

(c) intersecting lines

(d) none

The pair of linear equations x – 2y = 0 and 3x + 4y = 20 have: 

(a) one solution

(b) two solutions 

(c) many solutions

(d) no solution

The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages in years of the son and the father

respectively are:

(a) 4 and 24

(b) 6 and 36

(c) 5 and 30

(d) 7 and 42

For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = –16, represent coincident lines?

(a) \(1\over 2\)

(b) \(-1\over 2\)

(c) 2

(d) − 2

A pair of linear equations which has a unique solution x = 2, y = –3 is:

(a) x + y = –1, 2x – 3y = –5

(b) 2x + 5y = –11, 4x + 10y = –22

(c) 2x – y = 1, 3x + 2y = 0

(d) x – 4y – 14 = 0, 5x – y – 13 = 0

The pair of linear equations 2x + 5y = –11 and 5x + 15y = –44 has: 

(a) many solutions

(b) no solution

(c) one solution

(d) 2 solutions

The sum of the digits of a two-digit number is 9. If 27 is added to it, digits of the number get reversed. The number is:

(a) 63

(b) 72

(c) 81

(d) 36 

The pair of equations 5x – 15y = 8 and \(3x-9y=\frac{24}{5}\) has:  

(a) one solution

(b) two solutions

(c) infinitely many solutions

(d) no solution

If a pair of linear equations is consistent, then the lines will be:

(a) always intersecting

(b) always coincident

(c) intersecting or coincident

(d) parallel